Abstract: The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology, which continues to bear surprises. In this work, using spectroscopic imaging scanning tunneling microscopy, we discover a cascade of different symmetry-broken electronic states as a function of temperature in a new kagome superconductor, CsV3Sb5. At a temperature far above the superconducting transition Tc ~ 2.5 K, we reveal a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shape spectral gap opening at the Fermi level and an additional breaking of the six-fold rotation symmetry, which persists through the superconducting transition. This rotation symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the V kagome bands. Our experiments reveal a complex landscape of electronic states that can co-exist on a kagome lattice, and provide intriguing parallels to high-Tc superconductors and twisted bilayer graphene.

... read more

Topics: Fermi level (53%), Translational symmetry (53%), Frustration (52%) ... read more

More

43 results found

•••

Abstract: Kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, and Cs) exhibit intriguing superconductivity below $0.9\ensuremath{\sim}2.5\text{ }\text{ }\mathrm{K}$, a charge density wave (CDW) transition around $80\ensuremath{\sim}100\text{ }\text{ }\mathrm{K}$, and ${\mathbb{Z}}_{2}$ topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial ${\mathbb{Z}}_{2}$-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity ${T}_{c}$ in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our results provide essential knowledge toward understanding the superconductivity and topology in kagome metals.

... read more

Topics: Lattice (group) (75%), Coupling (probability) (73%), Charge density wave (52%) ... read more

63 Citations

•••

Abstract: The transition-metal-based kagome metals provide a versatile platform for correlated topological phases hosting various electronic instabilities. While superconductivity is rare in layered kagome compounds, its interplay with nontrivial topology could offer an engaging space to realize exotic excitations of quasiparticles. Here, we use scanning tunneling microscopy (STM) to study a newly discovered Z$_2$ topological kagome metal CsV$_3$Sb$_5$ with a superconducting ground state. We observe charge modulation associated with the opening of an energy gap near the Fermi level. When across single-unit-cell surface step edges, the intensity of this charge modulation exhibits a {\pi}-phase shift, suggesting a three-dimensional 2$\times$2$\times$2 charge density wave ordering. Interestingly, a robust zero-bias conductance peak is observed inside the superconducting vortex core on the Cs 2$\times$2 surfaces that does not split in a large distance when moving away from the vortex center, resembling the Majorana bound states arising from the superconducting Dirac surface states in Bi$_2$Te$_3$/NbSe$_2$ heterostructures. Our findings establish CsV$_3$Sb$_5$ as a promising candidate for realizing exotic excitations at the confluence of nontrivial lattice geometry, topology and multiple electronic orders.

... read more

Topics: Charge density wave (54%), Quasiparticle (52%), Fermi level (52%) ... read more

50 Citations

•••

Abstract: We argue that the topological charge density wave phase in the quasi-2D Kagome superconductor AV3Sb5 is a chiral flux phase. Considering the symmetry of the Kagome lattice, we show that the chiral flux phase has the lowest energy among those states which exhibit 2 × 2 charge orders observed experimentally. This state breaks the time-reversal symmetry and displays anomalous Hall effect. The explicit pattern of the density of state in real space is calculated. These results are supported by recent experiments and suggest that these materials are new platforms to investigate the interplay between topology, superconductivity and electron–electron correlations.

... read more

Topics: Density of states (55%), Superconductivity (53%), Topological quantum number (52%) ... read more

45 Citations

•••

Abstract: The recently discovered family of vanadium-based kagome metals with topological band structures offer a new opportunity to study frustrated, correlated and topological quantum states. These layered compounds are nonmagnetic and undergo charge density wave (CDW) transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in the vanadium-based kagome lattice CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. The differential conductance exhibits a V-shaped pairing gap about 0.5 meV below a transition temperature Tc about 2.3 K. Superconducting phase coherence is observed by Josephson effect and Cooper-pair tunneling to a superconducting tip. We find that CsV3Sb5 is a strong-coupling superconductor (2delta/kBTc about 5) and coexists with 4a0 unidirectional and 2x2 charge order. Remarkably, we discover a 4a0/3 bidirectional PDW accompanied by spatial modulations of the coherence peak and gap-depth in the tunneling conductance. We term the latter as a roton-PDW that can produce a commensurate vortex-antivortex lattice to account for the observed conductance modulations. Above Tc, we observe long-range ordered 4a0 unidirectional and 2a0 bidirectional CDW and a large V-shaped pseudogap in the density of state. Electron-phonon calculations attribute the 2x2 CDW to phonon softening induced structural reconstruction, but the phonon mediated pairing cannot describe the observed strong-coupling superconductor. Our findings show that electron correlations in the charge sector can drive the 4a0 unidirectional CDW, unconventional superconductivity, and roton-PDW with striking analogies to the phenomenology of cuprate high-Tc superconductors, and provide the groundwork for understanding their microscopic origins in the vanadium-based kagome superconductors.

... read more

Topics: Charge density wave (63%), Pseudogap (56%), Josephson effect (55%) ... read more

41 Citations

•••

Abstract: The recent discovery of topological charge density waves in the superconducting kagome metals $A$V${}_{3}$Sb${}_{5}$ ($A$=K, Rb, Cs) has attracted enormous attention Motivated by the experiments, the authors analyze here the interplay of real and imaginary charge density waves at the Van Hove singularity, but in a broader scope of general hexagonal lattices Phenomenological analysis uncovers a rich Haldane-model phase diagram The theoretical model sheds light on the experimental observations in these kagome metals and future experiments of hexagonal lattice materials

... read more

Topics: Van Hove singularity (62%), Hexagonal lattice (58%), Charge density (53%) ... read more

27 Citations

More

60 results found

••

Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

... read more

Topics: Local-density approximation (60%), Orbital-free density functional theory (57%), Density functional theory (56%) ... read more

117,932 Citations

••

Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ``metric'' and a special ``preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.

... read more

Topics: DIIS (51%)

64,484 Citations

•••

Abstract: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

... read more

Topics: Projector augmented wave method (66%), Pseudopotential (58%)

48,474 Citations

••

Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.

... read more

Topics: Cauchy stress tensor (53%)

46,297 Citations

••

Abstract: We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order Natoms2 scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.

... read more

Topics: Projector augmented wave method (55%), Conjugate gradient method (55%), Iterative method (54%) ... read more

40,008 Citations